What is the axis y=x^2+12x+6 ?

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axis y=x^2+12x+6

axis

y = x^{2} + 12 x + 6

x = - 6

Solution steps

y = x^{2} + 12 x + 6

Rewrite

y = x^{2} + 12 x + 6

in the standard form

4 \cdot \frac{1}{4} (y - (- 30)) = (x - (- 6))^{2}

Therefore parabola properties are:

(h, k) = (- 6, - 30), p = \frac{1}{4}

Parabola is of the form

4 p (y - k) = (x - h)^{2}

and is symmetric around the

y

-axis

Axis of symmetry is a line parallel to the

y

-axis which intersects the vertex:

x = - 6

y = - x^{2} + 120 x + 1300

(y - 2)^{2} = 3 (x - 5)

y = 0.5 (x + 1)^{2} - 2

y = x^{2} - 26 x + 65

y = \frac{1}{2} (x^{2} + 1) - \frac{3}{2} (x^{2} - 1)